(B) First,find the $\text{HCF}$ of $65$ and $117$ using prime factorization:$65 = 5 \times 13$$117 = 9 \times 13 = 3^2 \times 13$Therefore,$\text{HCF}

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(B) First,find the $\text{HCF}$ of $65$ and $117$ using prime factorization:$65 = 5 \times 13$$117 = 9 \times 13 = 3^2 \times 13$Therefore,$\text{HCF}(65, 117) = 13$.Given the equation: $\text{HCF}(65, 117) = 65m - 117$.Substitute the value of $\text{HCF}$:$13 = 65m - 117$$13 + 117 = 65m$$130 = 65m$$m = \frac{130}{65} = 2$.Thus,the value of $m$ is $2$.